Recent Developments in Low-Density Parity-Check Codes

Authors:
Wen-Ching Winnie Li;Min Lu;Chenying Wang
Affiliations:
Department of Mathematics, The Pennsylvania State University, USA PA 16802;Department of Mathematics, The Pennsylvania State University, USA PA 16802;Department of Mathematics, The Pennsylvania State University, USA PA 16802
Venue:
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Year:
2009

Citing 4
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Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
Low-density parity-check codes: asymptotic behavior and zeta functions

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On the Dimensions of Certain LDPC Codes Based on -Regular Bipartite Graphs

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Abstract

In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q -regular bipartite graphs with large girth constructed in [8]. The LDPC codes based on these graphs have attracted much attention. We show that the first few of these graphs are Ramanujan graphs.